Estimating Long Memory in Volatility

We consider semiparametric estimation of the memory parameter in a model that includes as special cases both long‐memory stochastic volatility and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long‐memory signal and a white noise. We consider periodogram‐based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional term to account for possible correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility by allowing the signal process to have a memory parameter d^*1/2. We show that the local Whittle estimator is consistent for d^*∈(0,1). We also show that the local Whittle estimator is asymptotically normal for d^*∈(0,3/4) and essentially recovers the optimal semiparametric rate of convergence for this problem. In particular, if the spectral density of the short‐memory component of the signal is sufficiently smooth, a convergence rate of n^2/5−δ for d^*∈(0,3/4) can be attained, where n is the sample size and δ>0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d^*=0. This yields a test for long memory in volatility.     

Adverse selection,moral hazard and propitious selection

We propose a simple model with preference-based adverse selection and moral hazard that formalizes the cherry picking/propitious selection argument. This argument assumes that individuals differ in risk aversion, potentially resulting in more risk averse agents buying more insurance while being less risky. The propitious selection argument is summarized by two properties: regularity (more risk averse agents exert more caution) and single-crossing (more risk averse agents have a higher willingness to pay for insurance). We show that these assumptions are incompatible with a pooling equilibrium, and that they do not imply a negative correlation between risk and insurance coverage at equilibrium.

Accounting for income distribution trends: A density function decomposition approach

This paper develops methods for decomposing changes in the income distribution using subgroup decompositions of the income density function. Overall changes are related to changes in subgroup shares and changes in subgroup densities, where the latter are broken down further using elementary transformations of individual incomes. These density decompositions are analogous to the widely-used decompositions of inequality indices by population subgroup, except that they summarize multiple features of the income distribution (using graphs), rather than focusing on a specific feature such as dispersion, and are not dependent on the choice of a specific summary index. Nonetheless, since inequality and poverty indices can be expressed as PDF functionals, our density-based methods can also be used to provide numerical decompositions of these. An application of the methods reveals the multi-faceted nature of UK income distribution trends during the 1980s.     

Ordres stochastiques et efficacité asymptotique des L-estimateurs

The efficiency of an estimator depends heavily on the tails of the distribution of the observations. Several partial orders have been defined to compare probability distributions according to their tails. In this paper we show that the asymptotic relative efficiency of two L-estimators with monotone weight functions is isotonic with respect to the partial orders defined by van Zwet (1964) and Lawrence (1975). We also give results concerning trimmed means.     

Political correctness and the study of racial differences

I tabulate international data showing Africans and Asians scoring at opposite ends of a continuum with Europeans falling in the middle. This Asian-European-African gradient occurs in mean scores on a long list of characteristics including brain size, crime, sex hormones, sexual behavior, personality, family stability, speed of physical maturation, twinning rate, and social organization. It seems to me that only evolutionary theories are able to fully explain the consistency of the pattern across so many variables. Theories about social inequalities and social problems may need to be revised in the light of this new information. This challenge to the social science orthodoxy brought political correctness out in force against me, some examples of which I document here. However, numerous benefits derive from studying race particularly in the field of medicine which I illustrate with special emphasis on AIDS. I conclude that if more scientists would speak openly about the views they now voice only in private, our world would become not only a safer place, but a more enlightened one as well.     

Optimized algorithms for computing Wilcoxon's T n,Wilcoxon's W m,n and Ansari-Bradley's A m,n statistics when m and n are small

Wilcoxon's signed rank sum test, Wilcoxon's rank sum test and the Ansari-Bradley rank test are three well-known distribution-free tests. When the sample size is large enough, the lower tail probabilities P 0 {T n /< = x} , P 0 {W m,n /< = x} and P 0 {A m,n /< = x} may be easily computed, under H 0 , using some normal approximations. When the size of the samples is too small, these normal approximations become insufficient. Therefore, the main goal of our work is to find some fast algorithms which compute the exact lower tail probabilities P 0 {T n /< = x}, P 0 {W m,n /< = x} and P 0 {A m,n /< = x} when the normal approximation is inefficient.     

Taux de résistance des tests de rang d'indépendance

The resistance of tests to acceptance and rejection of null hypotheses was denned and studied by Ylvisaker in the context of one-sample problems. This notion provides a measure of a test's resistance to outliers. In this paper, we propose an extension of this notion to rank-based tests of independence for bivariate random variables. We show, among other things, that Kendall's test of independence is more resistant than Spearman's test.     

Risk Management for Hazardous Materials Transportation: A Local Study in Lyons

A probabilistic risk assessment study has been undertaken in the French city of Lyons. The issue was to know whether it was justified to forbid hazardous material lorries in the city center and to divert them through the suburbs. Therefore, two routes, the City Center route and the Suburban route were compared. This paper describes the analysis and shows how the results were used in the decision-making process. It also lists the difficulties that are encountered when trying to incorporate formal risk analysis into actual decision-making processes. The risk analysis showed that rerouting is an effective option with respect to all criteria. The mathematical expectation of the number of deaths is divided by three, the reduction on the annual frequency of catastrophic accidents is even more important (about one order of magnitude for accidents involving more than 50 deaths). The spatial analysis proved that the risk was more evenly distributed along the Suburban route. However, the annual expected number of death is low: 0.5 in the worst case. So traditional decision-making approaches do not indicate the necessity of rerouting. Such a situation is believed to be typical for risk management of major hazards. In Lyons, the use of a very small risk aversion factor is sufficient to justify the rerouting option on a formal decision-aiding basis. This is rather unusual, but it is thought that the recognition of the importance of risk aversion by the decision-makers themselves is a very positive outcome from this study.